On the group of volume-preserving diffeomorphisms

Let $X$ be a manifold with volume element $\omega^n$. For any neighborhood $U\simeq\mathbf R^n$, let $D(U,\omega^n)$ be the group of diffeomorphisms of $X$ that are concentrated in $U$, and in this group let $D^0(U,\omega^n)$ be the component of the identity. We compute the inductive limit of the family $\{D^0(U,\omega^n)\}$ with respect to the natural inclusions $D^0(U,\omega^n)\hookrightarrow D^0(V,\omega^n)$ for $U\subset V$.
Bibliography: 15 titles.